The Network is devoted to anvanced research and training in the fields of Mathematical Physics and Stochastics, as well as some clossely related areas. The Network is a continuation of Centre for Mathematical Physics and Stochastics, which was funded from April 1998 to March 2003. The main fields of research in MaPhySto are Mathematical Physics (e.g. quantum mechanics, quantum field theory, quantum gravity, and quantum topology), Stochastics (e.g. stochastic analysis, computational stochastics, stochastic matrices, and free probability), with an emphasis on the interplay between these two fields. In the new period selected topics in biomathematics will be taken up. The work in Analytic Number Theory will also be continued. The activities in the Network include having PhD students and postdocs, organizing workshops, conference, summer schools, and concentrated advanced courses. These web pages contain detailed information on the activities of the Network. There is also access to the webpages from the Centre period.